Nitrocellulose lacquer is the finish of choice for most instruments.
www.reranch.com is a decent place to start, in that they've got supplies and instructions. Otherwise, search google for guitar refinish and you'll find lots of good links.
I'd recommend finishing some scrap wood to the same tolerances you want your bass first. Pick up a 6" piece of poplar from the local hardware store (because it's cheap and similar in grain to alder and basswood.) Get the various fillers, sealers, sandpapers, and get some generic spray lacquer if you don't want to waste a can of nitro. Then practice to get a super smooth finish. It's not really hard, but it does take some practice, and lots of patience.
If you decide you don't want to do it yourself, try taking the body to an auto finishing shop and see what they'll do for you.